UDK539.43:669.14.018.298 Original scientific article/Izvirni znanstveni članek ISSN 1580-2949 MTAEC9, 40(5)207(2006) THE BEHAVIOR OF FATIGUE-CRACKGROWTH IN SHIPBUILDING STEEL USING THE ESACRACK APPROACH MODELIRANJE RASTI UTRUJENOSTNE RAZPOKE JEKLA ZA LADIJSKE PLOČEVINE PO POSTOPKU ESACRACK Mira Shehu1, Peter Huebner2, Mimoza Cukalla3 1University Technologic "I.Qemali" Vlora, Albania 2Technische Bergakademie Freiberg, Germany Polytechnic University of Tirana, Albania her_shehuŽyahoo.com Prejem rokopisa – received: 2006-05-17; sprejem za objavo - accepted for publication: 2006-09-14 Crack growth-rate calculations with NASGRO 3.0 using a relationship called the ESACRACKapproach were developed by Forman and Newman at NASA. A simple assessment of the crack-growth analysis is given by the Paris law, called the analytic approach; however, for a complex case this assessment is conservative. In this paper we introduced and analyze the crack-growth curve for welded shipbuilding steel using the ESACRACKapproach by identifying the crack-opening function,f , the threshold stress-intensity factor, AKth, and the critical stress-intensity factor, KC. Keywords: fatigue-crack growth, structural steel, analytical approach ESACRACK Izvedli smo izračune hitrosti rasti utrujenostne razpoke z NASGRO 3.0 na osnovi tako imenovanega postopka ESACRACK, ki sta ga razvila Forman in Newman pri NASI. Enostavna ocena rasti utrujenostne razpoke je možna z analitičnim načinom, ki temelji na Parisovem zakonu. Vendar pa je v kompliciranih primerih ocena preveč konzervativna. V tem prispevku smo zato analizirali rast utrujenostne razpoke v konstrukcijskem jeklu, namenjenem za varjenje ladijske pločevine po postopku ESACRACK, ki temelji na funkciji odpiranja razpokef, mejni vrednosti faktorja intenzitete napetosti Kth in kritičnem faktorju intenzitete napetosti KC. Ključne besede: rast utrujenostne razpoke, konstrukcijsko jeklo, analitični postopek ESACRACK 1 INTRODUCTION Crack growth-rate calculations in NASGRO 3.0 use a relationship called the ESACRACK equation (1). This equation was developed by Forman and Newman and is described by: da dN C 1-f 1-R AK 1- AK KČ (1) where N is the number of applied fatigue cycles, a is the crack length, R is the stress ratio, da/dN is the crack-growth rate, f is the crack opening function, AK is the stress-intensity factor range, AKth is the threshold stress-intensity factor, C, n, p, and q are empirical constants, Kc is the critical stress-intensity factor, and Kmax is the maximum stress-intensity factor. 2 CRACK-OPENING FUNCTION The program incorporates fatigue-crack closure analysis for the calculation of the effect of the stress ratio, R, on the crack-growth rate under constant amplitude loading. The crack-opening function, f, for plastically induced crack closure has been defined by Newman using the following equation (2): K„ fmax( R ,A0 + A1 R + A 2R2 + A3R3) R>0 f K„ A 0 + A1 R -2 0, the crack-growth relationship reduces to: MATERIALI IN TEHNOLOGIJE 40 (2006) 5 207 M. SHEHU ET AL.: THE BEHAVIOR OF FATIGUE-CRACKGROWTH IN SHIPBUILDING STEEL Figure 1: Crack-growth function, f, versus R Slika 1: Funkcija rasti utrujenostne razpoke f, v odvisnosti od napetostnega razmerja R Figure 2: Dependence of ?Kth on R Slika 2: Odvisnost mejne vrednosti faktorja intenzitete napetosti ?Kth od napetostnega razmerja R da dN C\ AK\ AK J (3) K K J Note that freflects the amount of plastically induced crack closure. It should also be noted that Equation 3 (the closure-bypass option for R > 0) can be reduced to the Paris equation, da/dN = CŠAKf, by setting the parameters p and q equal to zero. In this case the threshold (AKth) and probably the fracture-toughness (Kc) asymptotes are retained as cut off values. 3 THRESHOLD STRESS-INTENSITY FACTOR RANGE Figure 3: Dependence of ?Kth/?Kth(LC) on crack size Slika 3: Odvisnost med razmerjem ?Kth/?Kth(LC) in velikostjo razpoke The threshold intensity factor range in Equation 1 is approximated by the following empirical equation 4: AK AKth = a + a 0 ) 1-f (1-A0)(1-R)) (1 + C th R) (4) The distribution for various R ratios can be controlled much better using the Cth (Cth+ ; Cth-) for negative and positive values of R, as in Figure 2. Figure 3 shows a plot of ?Kth/?Kth(LC) versus crack size, where ?Kth(LC) represents the "long-crack" fatigue threshold and the constant values are: a0 = 0,0381 mm, Cth+ = 1,9 dhe Cth– = 0,1. The parameter Rcl is the cut-off stress ratio, above which the threshold is assumed to be constant, and independent for negative and positive R values: Rcl = 0.62, Rpl = –1(plastic zone). Figure 4 shows a plot of ?K0 (threshold stress-intensity factor range at R = 0) versus yield stress for various steels with 235–960 MPa. Figure 4: Dependence of ?K0 on Re. Slika 4: Odvisnost med mejno vrednostjo faktorja intenzitete napetosti ?K0 (R = 0) in mejo tečenja Re za različna jekla v trdnostnem razredu med 235 MPa in 960 MPa When modeling the crack growth, in the HAZ (heat-affected zone) K0 is given by the upper values, as shown in Figure 4. q 1/2 a 208 MATERIALI IN TEHNOLOGIJE 40 (2006) 5 M. SHEHU ET AL.: THE BEHAVIOR OF FATIGUE-CRACKGROWTH IN SHIPBUILDING STEEL 3.1 The ESACRACK model for structural steel Using the model (1) for different steels with a yield stress range 235–885 MPa and for a stress ratio R = 0.1 shows that in the second zone we have a smaller difference with the model, which leads to a small difference in the crack growth, as indicated in Figure 5. 1.OOE-04 1.OOE-05 1.00E-07 10 AK/(MPaVm) 100 Figure 5: Fatigue-crack growth according to the model for three different steels and for the stress ratio R = 0 Slika 5: Model rasti utrujenostne razpoke treh različnih jekel pri napetostnem razmerju R = 0 As a recommendation II W 7 are given the crack-growth curve for the value of R = 0.1, but they are conservative, and for R = 0.5 we do not have a dependence for the crack-growth curve according to II W. 3.2 The ESACRACK model for different steels Figures 6, 7, 8, 9, 10,11 show for the steel S 885 in the HAZ (heat-affected zone), BM (base metal), WM (weld metal), S403, S283, S325 for different stress ratios R = 0.1, 0.3, 0.5, experimental and ESACRACKcrack-growth rate curves. Table 1 lists all the constants according to the ESACRACKmodel for the structural steel, shipbuilding steel and the welding joints with a = 2.5, Smax/o0 = 0.3 and Cth– = 0,1. 1.00E-03 ?K /(MPavm) Figure 6: Crack growth-rate curves for S885 steel (Base metal) and for three R ratios, modeling with ESACRACK Slika 6: Krivulje hitrosti rasti razpoke jekla vrste S885 (osnovni material) pri treh različnih napetostnih razmerjih R, modelirano z ESACRACK 1.00E-03 1.OOE-04 1.OOE-05 // ¦ R=0.1 Jy/ » R=0.3 o R=0.5 — ESACRACK HrB* ¦ jo JT m m pei m ?LTD AK/(MPaVm) Figure 7: Crack growth-rate curves for S885 steel (HAZl) and for three R ratios, modeling with ESACRACK Slika 7: Krivulje hitrosti rasti razpoke jekla vrste S885 (toplotno vplivana cona) pri treh različnih napetostnih razmerjih R, modelirano z ESACRACK Table 1: Constants according to the ESACRACKmodel for the structural steel, shipbuilding steel and the welding joints Tabela 1: Konstante konstrukcijskega jekla za ladijske pločevine in zvarne spoje, dobljene z modelom ESACRACK Steel AK 0 KC C n p q Cth+ Cth- S235 6.0 45 10–8 3 0.5 0.5 1.9 0.1 S460 6.5 70 10–8 3 0.5 0.5 1.9 0.1 S690 5.1 98 5·10-8 2.3 0.5 0.5 1.9 0.1 S325 8.7 40 5·10-8 3.3 0.25 0.25 3 0.25 S283 9.00 33 4·10–8 3.3 0.25 0.25 2 0.25 S403 8.7 30 4·10–8 2.2 0.25 0.25 2.7 0.25 S885 MB 5.11 106 2.4·10-8 2.7 0.25 0.25 1.9 0.1 S885HAZ 7.68 98 2·10–8 2.5 0.5 0.5 1 0.1 S885 WM 5.6 70 4·10–8 2.5 0.5 0.5 2.5 0.1 S960 MB 5.0 60 5·10-8 2.5 0.5 0.5 1.9 0.1 S960HAZ 7.8 75 4.5·10–9 3.1 0.6 0.25 1.9 0.1 S960 WM 5.5 62 1.3·10-8 2.8 0.5 0.5 1.9 0.1 .00E-03 .OOE-04 .OOE-05 .00E-06 .00E-06 .00E-07 0 00 .00E-06 .00E-07 MATERIALI IN TEHNOLOGIJE 40 (2006) 5 209 M. SHEHU ET AL.: THE BEHAVIOR OF FATIGUE-CRACKGROWTH IN SHIPBUILDING STEEL 1.00E-05 10 AK/(MPaVm) 100 Figure 8: Crack growth-rate curves for S885 steel (Weld metal) and for three R ratios, modeling with ESACRACK Slika 8: Krivulje hitrosti rasti razpoke jekla vrste S885 (material za varjenje) pri treh različnih napetostnih razmerjih R, modelirano z ESACRACK 1.00E-O4 1.00E-05 ¦ R = 0.1 » R = 0.3 • R = 0.5 — ESACRACK A ! IPČQ , , flit......... ?K /(MPavm) Figure 9: Crack growth-rate curves for shipbuilding steel S403 steel and for three R ratios, modeling with ESACRACK Slika 9: Krivulje hitrosti rasti razpoke konstrukcijskega jekla vrste S403 pri treh različnih napetostnih razmerjih R, modelirano z ESA-CRACK 1.00E-03 1.00E-04 1.00E-05 1.00E-06 1.00E-07 • R = 0.1 » R = 0.3 • R = 0.5 — ESACRACK • JEcČt fm p Ď ¦ •fi f * • i T 10 AK/(MPaVm) 100 Figure 10: Crack growth-rate curves for shipbuilding steel S283 steel and for three R ratios, modeling with ESACRACK Slika 10: Krivulje hitrosti rasti razpoke konstrukcijskega jekla vrste S238 pri treh različnih napetostnih razmerjih R, modelirano z ESA-CRACK 1.00E-03 1 1 00E-04 r 1.00E-07 ¦ R = 0.1 i R = 0.3 • R = 0.5 — ESACRACK !» f " 10 AK/(MPaVm) 100 Figure 11: Crack growth-rate curves for shipbuilding steel S325 steel and for three R ratios, modeling with ESACRACK Slika 11: Krivulje hitrosti rasti razpoke konstrukcijskega jekla vrste S325 pri treh različnih napetostnih razmerjih R, modelirano z ESA-CRACK 4 CONCLUSION The ESACRACKmodel used for the crack-growth curve gives a description of the crack-growth curve for different structural and shipbuilding steels, welding joints, and for different stress ratios, R, during cyclic loading. 5 REFERENCES 1 ESACRACK4.00 Manual 2 Newman, Jr., J. C., A Crack Opening date stress equation for fatigue crack growth, International Journal of Fracture, 24 (1984) 3, 31-R135. 3 K. Tanaka, Nakai, Y., Yamashita, M., Fatigue growth threshold of small cracks, International Journal of Fracture, 17 (1981) 5, 519–533 4 T. C. Llindley, Near threshold fatigue crack growth: experimental methods, mechanisms, and applications, subcritical crack growth due to fatigue, Stress Corrosion, and Creep, L. H. Larsson, ed., Elsevier Applied Science Publishers, New York, 1985, 167–213 5 R. O. Ritchie, Near threshold fatigue crack propagation in steels, International Metals Review, (1997), 205–230 6 P. Hübner, Schwingfestigkeit der hochfesten Baustähle StE885 und StE 960, Dissertation TU Bergakademie Freiberg, 1996 7 A. Hobbacher, Emphfehlungen zur Schwingfestigkeit geschweisster Verbindungen und Bauteile, IIW-document XIII-1539-96/ XV-845-96, DVS-Verlag, 1997 .00E-03 .00E-04 .00E-06 .00E-07 .00E-03 .00E-06 .00E-07 210 MATERIALI IN TEHNOLOGIJE 40 (2006) 5